Michael Magill

Demography and the Long-Run Predictability of the Stock Market

Stock market price/earnings ratios should be influenced by demography. Since demography is predictable, stock returns should be as well. We provide a simple stochastic OLG model with a cyclical structure that generates cyclical P/E ratios. We calibrate the model to roughly fit the cyclical features of historical P/E ratios.

Infinite Horizon Incomplete Markets

This paper extends the general equilibrium model with incomplete markets to an open-ended future, thereby providing a natural setting for analyzing problems in macroeconomics. Two concepts of equilibrium are defined that prevent agents from entering into Ponzi schemes: the first is based on debt constraints and the second is based on a transversality condition that limits the rate of growth of debt. Under the assumption that agents are impatient (Mackey continuity of preferences) and have a degree of impatience that is bounded below, the two concepts of equilibrium are shown to coincide and lead to existence of equilibrium. Copyright 1994 by The Econometric Society.

Generic inefficiency of stock market equilibrium when markets are incomplete

A stock market is a mechanism by which the ownership and control of firms is determined through the trading of securities. It is on this market that many of the major risks faced by society are shared through the exchange of securities and the production decisions that influence the present and future supply of resources are determined. If the overall structure of markets is incomplete can the stock market be expected to perform its role of exchanging risks and allocating investment efficiently? It is this question that we seek to answer.

Real effects of money in general equilibrium

Abstract This paper studies a simple stochastic general equilibrium model with money and nominal assets. We examine the role of money as a medium of exchange and as a store of value and give conditions under which local changes in the money supply lead to local changes in the equilibrium allocation.

Incomplete markets over an infinite horizon: Long-lived securities and speculative bubbles

Abstract This paper studies sequence economies over an infinite horizon with general security structures. Assumptions are given under which a pseudo-equilibrium exists for all economies and an equilibrium exists for a dense set of (appropriately parameterized) economies. Under these assumptions the indebtedness of the agents in equilibrium can be limited either by an explicit bound on their debts or by a transversality condition limiting the asymptotic growth of their debts. The qualitative properties of equilibrium prices of infinite-lived securities are studied: the prices of infinite-lived securities in zero net supply are shown to permit speculative bubbles and the existence of bubbles can affect the equilibrium allocation. The prices of securities in positive supply (equity contracts) cannot have speculative bubbles: the extent of speculation in this class of model is thus severely limited.

Some new results on the local stability of the process of capital accumulation

In the “Mecanique Analytique” (1788) Lagrange proved the following theorem. If the potential function of a conservative dynamical system attains a minimum (maximum) at a position of equilibrium then the motion in a neighborhood of this equilibrium point is stable (unstabZe).l In 1885 Poincare showed that if the potential function is made a function not only of the state of the system but also of an exogenous parameter and if the equilibria induced by the potential function are considered as functions of the parameter we obtain an equilibrium surface in the parameter-state space for which the stable and unstable branches are separated by bifurcation equilibria [50, pp. 43-551. If we combine these two ideas for a class of dynamical systems that arises in economic theory we obtain the beginings of a rich and interesting theory of economic dynamics. Such a theory has two parts, a short-run dynamics and a long-run dynamics. For a fixed value of the exogenous parameter the short-run dynamics classifies the equilibria associated with this parameter value into stable and unstable equilibria, and shows the local nature of the motion in the neighborhood of each equilibrium point when viewed in the state space. Such an analysis carried out for all feasible values of the parameter leads to a classification of the equilibrium manifold into stable and unstable submanifolds. A system with only stable equilibria will in general have associated with it a confinlrous long-run equilibrium manifold. When the exogenous parameter, taken as fixed in the short-run dynamics, is allowed to vary in a slow and systematic way, the system will trace out a trajectory along the equilibrium

Existence of equilibrium with incomplete markets

This paper proves a new fixed-point theorem for establishing generic existence of equilibrium with incomplete markets. The theorem can be stated in two equivalent forms: first as a fixed- point theorem on the Grassmanian of k-dimensional subspaces of Rn.: second as a generalisation of the Borsuk-Ulam theorem. The proof relies on the methods of algebraic topology: geometrically existence follows from the global twisting in the fibres of a naturally induced vector bundle.

Some Results on Comparative Statics under Uncertainty

This paper presents results on comparative statics for a class of decision problems under uncertainty. Necessary and sufficient conditions are derived for parameter changes and stochastically dominant shifts in the return in the two-asset portfolio problem. These results give conditions for the demand for money to be inversely related to the rate of interest. Further applications include the qualitive behavior of aggregate savings under uncertainty and the production decision of a firm facing price uncertainty. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

A geometric approach to a class of equilibrium existence theorems

In this paper we propose a general mathematical approach to existence problems in economics based on the geometry of vector bundles and the methods of intersection theory. The existence problem is formulated as: Does an approximate vector bundle admit a non-zero continuous section? The motivation and major application comes from incomplete market theory, where the appropriate vector bundle has, as one of the components of its base space, a Grassmanian manifold. Several general existence results are offered. One infinite dimensional generalization is included.

Characterisation of generically complete real asset structures

This paper compares the equilibrium allocations of a stochastic economy induced by two market structures: contingent markets and a sequential system of spot and real asset markets. We exhibit a regularity condition on the asset structure which we prove to be a necessary and sufficient condition for the equilibrium allocations for the two market structures to coincide generically.